Algorithm 3: Stable task assignment algorithm with adjustable bids

Step 1: Initialization

1: $m=1, \forall s_i\in \mathcal{S}, t_k\in \mathcal{T}, p^m(i,k)=p_{\max }(i,k), fla{g}_i=1$

Step 2: Buyer and seller’s transaction phase

2: while ${\displaystyle \sum _{s_i\in S}f}la{g}_i>0$ does

3: for $s_i\in \mathcal{S}$ do

4:    first calculate $r(i, k)=r(s_i)\cap r(t_k)$, then calculate $c(i, k)$ and $q(i, k)$ from $r(i, k)$, then calculate $w^m\left(s_i\right)=\left\{t_k\mid p^m(i,k)\ge c(i,k), \forall t_k\in \mathcal{T}\right\}$

5:    if $w^m\left(s_i\right)\ne \varnothing$, then

6:        for $\forall t_k\in w^m\left(s_i\right)$ do

7:        the user $s_i$, sends the solicitation packages $p^m(i, k)$ and $q(i, k)$ to the task. $t_k$

8:        end for

9:    end if

10: end for

11: for $t_k\in \mathcal{T}$ do

12:    $t_k$ after collecting the bid packets sent by sellers, use $w^m(t_k)$ to indicate the set of sellers for the bid packets received at $t_k$ use the DP algorithm to select the sellers from $w^m(t_k)$ and reject the unselected sellers

13: end for

14: for $\forall t_k\in \mathcal{T}, s_i\in w^m\left(t_k\right)$ do

15:    if $s_i$, is rejected by $t_k$ and $p^m(i, k)>c(i, k)$, then

16:        $p^{m+1}(i, k)=\max \left\{p^m(i, k)-{\delta }_i, c(i, k)\right\}$

17:    else, if $t_k$, or $p^m(i, k)=c(i, k)$ receives $s_i$, then

18:        $p^{m+1}(i, k)=p^m(i, k)$

19:    end if

20:    $fla{g}_i=0$

21:    if $p^{m+1}(i, k)\ne p^m(i, k)$, then

22:        $fla{g}_i=1$

23:    end if

24: end for

25: $m=m+1$

26: end while